Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #436×C73 ⋊ C2 |
| Sylow | C73 ⋊ #3330 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D292 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #436×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #436 | D73 |
| hypocenter | C73 | #3330 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #436 | |
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|a^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^72,c^b=cg,d^b=de,f^c=fg,h^c=h^721037 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33075591, #33075593, #33075651, … |
| maximal normal subgroup of | #33075591, #33075593, #33075651, … |
| maximal quotient of | #33101637, #33102408, #33103278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 16816);